Search games by PC platform and you can find several free games on Steam/Itch.io/GameJolt. You can also search games by WEB, all of them are free.
Epic Games has been giving away games every week too, most of them are just okay but there are some good ones in there. You might get your hands on something to run at some point.
I’ve never tried speedrunning Runescape, but it’s fun and free.
https://www.moddb.com/games/area-511/downloads/area-51-pc-version
Area 51 from 2005 its abandonware now and its a free first person shooter. Its very good to, think doom 3 but with aliens. Don't forget to download the update patch or the game will crash.
Also, in addition to Web as somebody mentioned above, lots of games under iOS or Android are free.
Check out abandonware. I'm a big fan of the MechWarrior series and everything in the series besides the most recent releases has been abandoned. Even if MW isn't your cup 'o tea, there's lots of old PC games to find.
Hellpoint: The Thespian Feast is a free game on Steam. Commonly and incorrectly referred to as a demo, it's actually a sequel chapter to the core Hellpoint game. But it exists entirely on its own.
In addition to the area 51 game I posted there are quite a few dan maku bullet hell shmups out there for free all you have to do is search google. Although shmups themselves don't make for great speedruns you can still technically run them.
https://store.steampowered.com/app/321330/ENYO_Arcade
Fast paced 2d platformer with movement that's 90% very streamlined Super Metroid 10% rocket / recoil jumping, has glitches, has skips, has multiple viable routes, has extensive optimization potential both in the routing and movement execution.
Here's a mediocre attempt at speedrunning the second level.
Check out Were.Wolf, it's a free great platformer game on Itch.io that I found a weeks or so ago. https://yrgo-game-creator.itch.io/werewolf
Here's the leaderboards: https://www.speedrun.com/were_wolf
